Adjusting for centre heterogeneity in multicentre clinical trials with a time‒to‒event outcome

Conducting a clinical trial at multiple study centres raises the issue of whether and how to adjust for centre heterogeneity in the statistical analysis. In this paper, we address this issue for multicentre clinical trials with a time?to?event outcome. Based on simulations, we show that the current practice of ignoring centre heterogeneity can be seriously misleading, and we illustrate the performances of the frailty modelling approach over competing methods. A special attention is paid to the problem of misspecification of the frailty distribution. The appendix provides sample codes in R and in SAS to perform the analyses in this paper. Copyright © 2014 John Wiley & Sons, Ltd.     

Mean square prediction error for long-memory processes

ARFIMA (p, d, q) processes. In particular we obtain the (asymptotic) mean square prediction error when the parameters of the process are either known or estimated in the cases both of correct and misspecified model. Some Monte Carlo experiments confirm the validity of the asymptotic results. Received: August 6, 1999; revised version: June 26, 2000     

A new method for estimating finite-population quantiles using auxiliary information

A computationally simple method for estimating finite-population quantiles in the presence of auxiliary information is proposed. An algorithm is also found for implementing related approaches for estimating quantiles, including that of Rao et al. (1990), obtained from inverting difference-type estimators of the distribution function. The proposed estimation procedure can be seen as a one-step iteration of the suggested algorithm and is asymptotically equivalent to the limiting estimator. In particular, the proposed method yields a simple and efficient way of approximating Rao et al.'s estimator. Simulation studies based on two real populations show that the approximation can be very satisfactory even for small to moderate samples.     

A note on the likelihood-ratio statistic under model misspecification

Following Viraswami and Reid (1996), higher-order results under model misspecification are obtained for the likelihood-ratio statistic and the adjusted likelihood-ratio statistic, for the case of a scalar parameter. An improved version of the adjusted likelihood-ratio statistic is suggested.     

A semiparametric extended hazard regression model with time-dependent covariates

We introduce a general class of semiparametric hazard regression models, called extended hazard (EH) models, that are designed to accommodate various survival schemes with time-dependent covariates. The EH model contains both the Cox model and the accelerated failure time (AFT) model as its subclasses so that we can use this nested structure to perform model selection between the Cox model and the AFT model. A class of estimating equations using counting process and martingale techniques is developed to estimate the regression parameters of the proposed model. The performance of the estimating procedure and the impact of model misspecification are assessed through simulation studies. Two data examples, Stanford heart transplant data and Mediterranean fruit flies, egg-laying data, are used to demonstrate the usefulness of the EH model.     

Fitting models to data: Interaction versus polynomial? your choice

Polynomials are widely used for fitting models empirically to data. Low-degree polynomials (specifically, degrees 1, 2, and at most 3) have stood the test of time by proving their versatility when it comes to fitting a wide variety of different surface shapes over limited regions of interest. However, when faced with modeling a surface over an experimental region whose boundaries extend beyond some localized neighborhood or limited-sized region of interest, a polynomial of degree 2, or even of degree 3, may not be adequate. For this situation we propose fitting an interaction model which is a reduced form of higher-degree polynomial. Some examples of actual experiments are presented to illustrate the improvement in fit by an interaction model over that of a standard polynomial, even for response surfaces with uncomplicated shapes.     

Properties of robust m-estimators for poisson and negative binomial data ∗

We investigate robust M-estimators of location and over-dispersion for independent and identically distributed samples from Poisson and Negative Binomial (NB)distributions. We focus on asymptotic and small-sample efficiencies, outlier-induced biases, and biases caused by model mis-specification. This is important information for assessing the practical utility of the estimation method. Our results demonstrate that resonably efficient estimation of location and over-dispersion parameters for count data is possible with samples sizes as small as n=25. The sensitivity of these stimators, especially when the amount of over-dispersion is small. We aslo conclude that serious biases result when using robust Poisson M-estimation with NB data. The biases are less serious when using robust NB M-estimation with Poisson data.     

On the Use of Buy Up as a Model of Customer Choice in Revenue Management

We consider settings in which a revenue manager controls bookings over a sequence of flights. The revenue manager uses a buy‐up model to select booking limits and updates estimates of the model parameters as data are accumulated. The buy‐up model we consider is based upon a simple model of customer choice, wherein each low‐fare customer who is not able to purchase a low‐fare ticket will, with a fixed probability, “buy up” to the high fare, independent of everything else. We analyze the evolution of the parameter estimates (e.g., the buy‐up probability) and chosen booking limits in situations where the buy‐up model is misspecified, that is, in situations where there is no setting of its parameters for which its objective function gives an accurate representation of expected revenue as a function of the booking limit. The analysis is motivated by the common situation in which a revenue manager does not know precisely how customers behave but nevertheless uses a parametric model to make decisions. Under some assumptions, we prove that the booking limits and parameter estimates converge and we compare the actual expected revenue at the limiting values with that associated with the booking limits that would be chosen if the revenue manager knew the actual behavior of customers. The analysis shows that the buy‐up model often works reasonably well even when it is misspecified, and also reveals the importance of understanding how parameter estimates of misspecified models vary as functions of decisions.     

On measuring sensitivity to parametric model misspecification

In settings where parametric inference is inconsistent under model misspecification, the discrepancy between correct and misspecified inferences is compared with the discrepancy between correct and misspecified models. To make the comparison tractable, large sample and small misspecification approximations are employed. The ratio of the approximate discrepancy between inferences to the approximate discrepancy between models is regarded as a relative measure of sensitivity to model misspecification. The maximum ratio over a family of correct distributions is determined as a measure of worst case sensitivity. As well, the distribution producing this maximum can be examined, to see how a particular combination of a parametric family and estimand is susceptible to model misspecifications.     

Overdispersed poisson regression models for studies of air pollution and human health

This paper presents results from a simulation study motivated by a recent study of the relationships between ambient levels of air pollution and human health in the community of Prince George, British Columbia. The simulation study was designed to evaluate the performance of methods based on overdispersed Poisson regression models for the analysis of series of count data. Aspects addressed include estimation of the dispersion parameter, estimation of regression coefficients and their standard errors, and the performance of model selection tests. The effects of varying amounts of overdispersion and differing underlying variance structure on this performance were of particular interest. This study is related to work reported by Breslow (1990) although the context is quite different. Preliminary work led to the conclusion that estimation of the dispersion parameter should be based on Pearson's chi-square statistic rather than the Poisson deviance. Regression coefficients are well estimated, even in the présence of substantial overdispersion and when the model for the variance function is incorrectly specified. Despite potential greater variability, the empirical estimator of the covariance matrix is preferred because the model-based estimator is unreliable in general. When the model for the variance function is incorrect, model-based test statistics may perform poorly, in sharp contrast to empirical test statistics, which performed very well in this study.